The American Ballet Theatre today reached an agreement-in-principle to hire for the fourth time the often-troubled superstar ballerina Gelsey Kirkland. ABT said an announcement of the agreement, which would take effect immediately, was anticipated for Thursday afternoon.

Kirkland is expected to begin rehearsals immediately and is likely to perform with ABT when the company gives its first performances of its labor-dispute-shortened season beginning Jan. 19 at the Kennedy Center.

Kirkland previously has joined and then departed from ABT at least three times. She was hired in 1974 at the request of Mikhail Baryshnikov. She resigned in 1979 for personal reasons. She rejoined the company the following season, but was fired in December 1980 of the eve of ABT's Kennedy Center engagement for chronic failure to appear for rehearsals.

In spring 1981, during an ABT season at the Kennedy Center, Kirkland again rejoined the company.

She was let go again in the summer of 1981.

ABT executive director Herman E. Krawitz last night confirmed that "The rumor of her return is correct." Krawitz said, "A contract is being prepared" which contains the terms of the arrangement that Kirkland accepted today. Krawitz said he expects it will be signed Thursday.

The only other comment the ABT executive director made about the company's stunning coup was to say that Kirkland's rehiring resulted from "Our constant desire for great talent . . . and our belief that it is worth pursuing that talent."

Sources close to ABT said that Kirkland, Krawitz and ABT artistic director Baryshnikov met today to close the deal.

"Gelsey knows that we want her," one ABT source said. The terms and the length of the contract were not available, but the source said, "We're just going to see how it works out."

Kirkland could not be reached for comment.

Meanwhile, Kirkland and Baryshnikov will appear together in a nationally televised repeat performance of ABT's "The Nutcracker," scheduled to air next month on PBS.